Percentage techniques & examples checklist
If you’re asked to find the percentage of an amount, divide the percentage by 100 (by moving the decimal point two places to the left) and multiply it by the amount you’re finding the percentage of. Example Find 85% of 240. 85/100 = 0.85 0.85 x 240 = 204
If you’re asked to increase an amount by a certain percentage, multiply the amount by one plus the decimal equivalent of the percentage. Example Increase 240 by 20% 240 x (1 + 0.2) = 240 x 1.2 = 288
If you’re asked to decrease an amount by a certain percentage, then work out what percentage you’ll have left at the end, then find this amount using the first technique Example Decrease 240 by 30% We will have 70% after the reduction, so the answer is obtained by working out 70% of 240. 240 x 0.7 = 168
To find one number as a percentage of another, divide the first number by the second number, and multiply by 100 Example Find 120 as a percentage of 240. (120/240) x 100 = 50%
To work out the percentage increase/decrease of two numbers, divide the change by the original and multiply by 100 Example
Find the percentage change from 380 to 240. Change = 380 – 240 = 140 Original = 380 (Change/original) x 100 = (140/380) x 100 = 36.8% decrease. If the amount gets larger, it’s an increase. If it gets smaller it’s a decrease.
To work out reverse percentages you need to consider what percentage of the original the current amount represents. Then divide the amount by that percentage and multiply the result by 100. Example After a 20% reduction, a coat costs 36 pounds. Work out the original cost of the coat. The current price of the coat represents 80% of the original price (since 20% has been knocked off). So we divide by 80 and times by 100. (36/80) x 100 = 45 pounds Example 2 After VAT at 15%, a CD costs 14 pounds, work out the cost before VAT was added. The current price of the CD represents 115% of the original price (since 15% was added on) so we divide by 115 and times by 100 (14/115) x 100 = 12.17 pounds
To find compound percentages, we consider what decimal we need to multiply to get the first result, we then raise this decimal to the number of times we wish to find the percentage. Finally we multiply this new number by the original amount. Example The value of an antique increases by 2% every year. The current value is 1000 pounds, find the value after 5 years. To find the value after one year we would multiply by 1.02. Since we need to find the value after 5 years we raise 1.02 to the power of 5 and multiply this by 1000 (the original amount) 1000 x (1.02)5 = 1104.08 pounds Example 2 Due to a recession, the value of a share goes down by 3% every year. A share is currently worth 9 pounds, find its worth after 3 years.
To find its value after one year we would multiply 9 by 0.97. But since we want to find the value after 3 years we raise 0.97 to the power of 3 and then multiply it by our amount. (0.97)3 x 9 = 8.21 pounds